**Date:** September 29 2022

**Summary:** A simple overview on what a family of sets actually is

**Keywords:** ##summary #set #family #subset #archive

Not Available

I am having trouble reading some set theoretic notation. Hoping by gaining better familiarity with family of sets, I can understand notation better.

In brief, a family of sets could be the following:

**Definition 1:** A family of sets, $F$, could be a set of subsets over a set $X$. An example of this would be the following scenario:

Let $X = {1, 2, 3, 4}$

$F = \{\{\emptyset\}, \{1, 2 \},\{3, 4\}\}$ $F$is non-exhaustive as there could be more subsets derived from $X$.

**Definition 2:** A family of sets, $F$, could be a set of sets where each set is independent from the others. An example of this would be the following scenario:

Let $A = \{1, 2, 3\}$, $B = \{4, 5, 6\}$, and $C = \{2, 4, 6\}$

$F = \{A, B, C\} = \{\{1, 2, 3\}, \{4, 5, 6\}, \{2, 4, 6\}\}$Zelko, Jacob. *Family of Sets*. https://jacobzelko.com/09302022033236-family-sets. September 29 2022.

CC BY-SA 4.0 Jacob Zelko. Last modified: July 16, 2023.
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